LECTURE SIX

System viewed as interconnection of operation: This article is dealt in detail again in chapter 2/3. This article basically deals with system connected in series or parallel. Further these systems are connected with adders/subtractor, multipliers etc.

Properties of system:

The discrete time system: The discrete time system is a device which accepts a discrete time signal as its input, transforms it to another desirable discrete time signal at its output as shown in figure 1.20

Fig 1.2 DT system Stability A system is stable if „bounded input results in a bounded output‟. This condition, denoted by BIBO, can be represented by:

…….(1.42) Hence, a finite input should produce a finite output, if the system is stable. Some examples of stable and unstable systems are given in figure 1.21 Fig 1.21 Examples for system stability

Memory The system is memory-less if its instantaneous output depends only on the current input. In memory-less systems, the output does not depend on the previous or the future input. Examples of memory less systems:

Causality: A system is causal, if its output at any instant depends on the current and past values of input. The output of a causal system does not depend on the future values of input. This can be represented as:

y[n] F x[m]for m n

For a causal system, the output should occur only after the input is applied, hence, x[n] 0 for n 0 implies y[n] 0 for n 0 All physical systems are causal (examples in figure 7.5). Non-causal systems do not exist. This classification of a system may seem redundant. But, it is not so. This is because, sometimes, it may be necessary to design systems for given specifications. When a system design problem is attempted, it becomes necessary to test the causality of the system, which if not satisfied, cannot be realized by any means. Hypothetical examples of non-causal systems are given in figure below.

Invertibility: A system is invertible if, Linearity: The system is a device which accepts a signal, transforms it to another desirable signal, and is available at its output. We give the signal to the system, because the output is s

Time invariance: A system is time invariant, if its output depends on the input applied, and not on the time of application of the input. Hence, time invariant systems, give delayed outputs for delayed inputs.